An empirical study into the theory of unidimensional unfolding

This article is the second in the series on unidimensional unfolding. Its aim was to test the quantitative component of Coombs's (1964) theory via an empirical application to subjective control in gambling behavior (Dickerson and Baron, 2000). It was found that approximately 96% of judgments upon bilateral stimulus pairs were as predicted by the theory of unidimensional unfolding. The double cancellation axiom of the theory of axiomatic conjoint measurement (ACM) (Krantz, Luce, Suppes and Tversky, 1971) was satisfied by the interstimulus midpoint order obtained from these judgments. These results supported previous unfolding studies on attitudes (Johnson, 2001; Michell, 1994). Exponential and linear relationships were found between the transformed scaling solutions of Coombs's (1964) theory and the SHCMpp (Andrich, 1995). The implications of these results were discussed. Additionally, the article presented both a formal theory of item construction (Michell, 1994) and an accessible demonstration of the Goode's algorithm scaling procedure.